A statistical procedure for modelling the cumulative effect of multiple
collisions in particle simulations is presented. The procedure approximates
the probability density function (PDF) of the final scattering angle and that
of the particle net displacement by parametric functions. Formulae for
determining the moments of the exact PDFs as a function of the statistics of
a single collision event are derived. Using these formulae, the parametric
functions can be fitted to yield the same first moments as the real
distributions. Therefore, in contrast to other approaches where after one
iteration the error in the first moments depends on the number of collisions
modelled, the present model provides always the right moments.
Correlation between the scattering angle and the displacement of the particle
is also considered and enforced by means of a Gaussian copula.